2.find four consecutive odd integers such that the sum of the two largest integers subtract from twice the sum of the two smallest integers is 96
Let the four consecutive odd integers be: x, x+2, x+4, x+6
The sum of the two largest integers: (x+4) + (x+6) = 2x + 10
Twice the sum of the two smallest integers: 2(x + x+2) = 4x + 4
The equation formed is: (2x + 10) - (4x + 4) = 96
Solving the equation:
2x + 10 - 4x - 4 = 96
-2x + 6 = 96
-2x = 90
x = -45
Plugging x back in to find the four consecutive odd integers:
-45, -43, -41, -39
Therefore, the four consecutive odd integers are -45, -43, -41, and -39.